Calculation and Analysis of the Pulse Response of Spatially Non-Invariant Projection Systems

  • Yu. V. ChuguiEmail author
Optical Information Technologies


Characteristics of spatially non-invariant telecentric projection systems, which are widely used in practice, are considered within the framework of wave optics. In the class of the Fresnel functions, the pulse response of the system is precisely calculated for various values of the projection objective and filter apertures. It is found that the response consists of two components, which determine the invariant and non-invariant properties of the system, respectively. Based on the approximation of the Fresnel function by elementary functions proposed previously by the author, an analytical expression for the pulse response is derived for the first time, and the response behavior is studied for various relationships of the objective and filter apertures. The correctness of choosing the parameters of the known quasi-invariant optical systems is analyzed. Recommendations on choosing the filter aperture are given to improve their spatially invariant characteristics. In contrast to available optical and geometrical methods, the proposed approach allows one to obtain reliable information about the character of wave field transformations in the considered systems.


light diffraction telecentric projection systems Fourier optics dimensional inspection 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. W. Goodman, Introduction to Fourier Optics (New York, 1968).Google Scholar
  2. 2.
    Yu. V. Chugui, “Fourier Optics of Constant-Thickness Three-Dimensional Objects on the Basis of Diffraction Models,” Avtometriya 53 (5), 90–105 (2017) [Optoelectron., Instrum. Data Process. 53 (5), 494–507 (2017)].Google Scholar
  3. 3.
    H. Stephen, “Quasigeometric Approach to the Fourier Analysis of Imaging Lenses,” JOSA 61 (9), 1428–1429 (1971).Google Scholar
  4. 4.
    H. H. Arsenault and N. Brousseau, “Space Variance in Quasi-Linear Coherent Optical Processors,” JOSA 63 (5), 555–558 (1973).ADSCrossRefGoogle Scholar
  5. 5.
    Reference Book on Special Functions, edited by M. Abramov and I. Stishin (Nauka, Moscow, 1979) [in Russian].Google Scholar
  6. 6.
    Yu. V. Chugui and B. E. Krivenkov, “Fraunhofer Diffraction by Volumetric Bodies of Constant Thickness,” JOSA 6 (5), 617–626 (1973).CrossRefGoogle Scholar
  7. 7.
    B. N. Begunov, N. P. Zakaznov, S. I. Kiryushin, and V. I. Kuzichev, Theory of Optical Systems (Mashinostroenie, Moscow, 1981) [in Russian].Google Scholar
  8. 8.
    A. Ghatak, Optics, 3-rd edition (Tata McGraw-Hill, New Delhi, 2005).Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Technological Design Institute of Scientific Instrument EngineeringSiberian Branch, Russian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations